Causal Effects and Experiments

GVPT399F: Power, Politics, and Data

Causes and effects

Our goal is to better understand what factors lead to certain outcomes of interest.

  • Does increasing the number of voting booths close to a potential voter make that person more likely to vote?

  • Do peace treaties signed with factionalized rebel groups more often lead to a return to conflict than those signed with a single, cohesive group?

  • Does trade between two countries make war between them less likely?

Causes and effects

These are causal statements:

  • More local voting booths \(\rightarrow\) More likely to vote

  • More factionalization \(\rightarrow\) More likely to restart conflict

  • Trade \(\rightarrow\) Less likely to go to war

How to identify causes and their effects

Proving that changes to one factor cause changes to another is very tricky!

  • Need to account for all the other factors

The efficacy of international election monitors

Do international monitors cause less election-day fraud in democratic elections?

  • Number of elections monitored by international observers exploded throughout the 2000s

  • But do monitors increase the chances the election will be free and fair?

  • In other words, are they effective?

The efficacy of international election monitors

Dr Susan Hyde set out to answer this very question. From her article (page 39):

If the presence of international observers causes a reduction in election-day fraud, the effect of observers should be visible at the subnational level by comparing polling stations that were visited by observers with those that were not visited. More specifically, if international monitoring reduces electionday fraud directly, all else held equal, the cheating parties should gain less of their ill-gotten vote share in polling stations that were visited by international monitors.

Causal relationships

Refers to the directional connection between a change in one variable and a corresponding change in another.

  • The direction matters!

  • Treatment variable: the variable causing changes to another variable.

  • Outcome variable: the variable changing as a result of changes to another variable (the treatment).

Treatment and outcome variables

We want to test whether the presence of international monitors (treatment) leads to less election day fraud (outcome).

International election monitors present at polling stations \(\rightarrow\) Less election-day fraud at that station

Treatment variable

At any given polling station in any given election, monitors may be: 1) present, or 2) not present.

Two different conditions:

  • Treatment: condition with treatment (monitors are present)

  • Control: condition without treatment (monitors are not present)

Outcome variable

At any given polling station in any given election, fraud may: 1) occur, or 2) not occur.

Observing our outcome

Sometimes it can be hard to observe our outcome of interest.

  • How might we see all election-day fraud?

  • How might we measure it?

Observing our outcome

Hyde’s answer: vote-share!

International election monitors present at polling stations \(\rightarrow\) Less election-day fraud at that station \(\rightarrow\) Lower vote-share for the cheating party

Individual causal effects

We want to know whether the treatment causes a change in our outcome of interest.

What might this look like in the real world?

  • Imagine we are looking at a specific election

  • Five polling stations

Parallel worlds

Hypothetical election

ID Monitored vote % Non-monitored vote %
1 28.12 93.04
2 49.22 83.60
3 59.85 83.81
4 33.39 87.76
5 16.90 91.69

Individual effects

The only difference between these two conditions is the presence of international monitors!

  • The difference between vote shares under these conditions is caused by the monitors.

Individual effects

ID Monitored vote % Non-monitored vote % Difference (%)
1 28.12 93.04 -64.92
2 49.22 83.60 -34.38
3 59.85 83.81 -23.96
4 33.39 87.76 -54.37
5 16.90 91.69 -74.79

No parallel worlds

Sadly for us, we cannot create parallel worlds…

What now?

ID Monitored Monitored vote % Non-monitored vote % Difference
1 0 NA 93.04 NA
2 0 NA 83.60 NA
3 0 NA 83.81 NA
4 1 33.39 NA NA
5 1 16.90 NA NA

Average causal effects

We need to move away from looking at individuals and start to look for patterns in our group.

Back to our parallel worlds

ID Monitored vote % Non-monitored vote % Difference
1 28.12 93.04 -64.92
2 49.22 83.60 -34.38
3 59.85 83.81 -23.96
4 33.39 87.76 -54.37
5 16.90 91.69 -74.79

Difference of averages across all individuals

What was the average vote share received in each world?

Avg. monitored vote % Avg. non-monitored vote % Difference
37.5 87.98 -50.48

Back to reality

ID Monitored Monitored vote % Non-monitored vote % Difference
1 0 NA 93.04 NA
2 0 NA 83.60 NA
3 0 NA 83.81 NA
4 1 33.39 NA NA
5 1 16.90 NA NA

Difference-of-means

What was the average vote share received in each group?

Avg. monitored vote % Avg. non-monitored vote % Difference
25.14 86.82 -61.67

How on Earth does this work so well?

Randomization!

  • Monitors were assigned to polling stations randomly (for example, with the flip of a coin)

  • This created two groups of stations that were roughly identical on average to one another prior to treatment

  • This mimics what happens when we split our world into two (creating two literally identical groups)

Our goal

We want two groups that are completely identical to one another prior to treatment.

  • This allows us to compare their outcomes after treatment and claim that the treatment caused differences in those outcomes (if any differences exist)

Our goal

Next best thing

Instead, we should try to make two groups that are as similar as possible to each other prior to treatment.

The magic of randomization

Perfectly random assignment does this very well!

Don’t take my word for it

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Our group

ID Height Weight Eye colour
1 164.26 52.92 Green
2 166.89 84.08 Grey
3 173.48 76.97 Brown
4 170.48 84.42 Blue
5 175.38 86.80 Green
6 167.74 73.26 Blue
7 176.89 78.91 Blue
8 170.59 86.85 Brown
9 176.90 84.77 Blue
10 171.01 69.88 Grey
11 168.57 71.46 Blue
12 170.08 83.52 Green
13 169.57 69.79 Grey
14 168.58 74.14 Grey
15 167.81 75.07 Grey
16 171.51 60.62 Brown
17 170.24 60.93 Brown
18 171.78 74.47 Grey
19 180.18 93.82 Blue
20 173.31 83.43 Green
21 161.92 99.96 Grey
22 173.14 74.92 Green
23 175.69 79.47 Brown
24 181.84 94.84 Green
25 165.85 91.22 Grey
26 168.48 76.40 Green
27 178.39 68.96 Grey
28 174.01 83.72 Brown
29 181.95 78.79 Brown
30 171.50 73.69 Blue
31 158.98 88.57 Green
32 175.80 82.91 Grey
33 177.61 62.68 Green
34 170.61 66.02 Blue
35 165.31 70.63 Blue
36 171.15 65.33 Brown
37 175.04 88.20 Grey
38 172.63 66.92 Grey
39 174.24 77.46 Grey
40 171.23 72.70 Green
41 181.85 76.38 Brown
42 169.84 72.25 Brown
43 178.83 86.12 Grey
44 180.32 69.69 Brown
45 168.65 72.67 Green
46 162.35 57.10 Blue
47 152.79 78.98 Grey
48 172.59 83.20 Green
49 173.95 75.92 Blue
50 175.94 90.79 Green
51 167.77 68.77 Green
52 164.13 70.63 Blue
53 175.30 75.30 Grey
54 168.81 88.19 Green
55 167.47 83.78 Brown
56 168.07 74.57 Blue
57 157.69 60.87 Blue
58 164.92 74.49 Brown
59 171.48 75.50 Brown
60 157.84 79.47 Green
61 174.07 86.33 Brown
62 161.46 70.05 Grey
63 170.23 80.54 Blue
64 170.85 90.98 Grey
65 178.94 74.48 Grey
66 173.93 64.49 Blue
67 173.22 67.79 Brown
68 175.84 71.85 Blue
69 170.90 93.90 Green
70 160.68 69.41 Blue
71 171.09 79.61 Blue
72 180.43 79.34 Green
73 163.23 107.84 Brown
74 163.43 72.68 Grey
75 166.36 92.99 Green
76 168.49 91.05 Brown
77 174.75 84.66 Grey
78 162.17 91.25 Brown
79 166.22 93.94 Blue
80 164.78 89.26 Green
81 169.83 67.22 Blue
82 166.89 67.41 Grey
83 167.84 71.53 Grey
84 170.30 64.05 Brown
85 179.13 72.42 Green
86 161.91 71.91 Brown
87 180.92 85.47 Grey
88 168.68 63.92 Green
89 176.12 77.45 Brown
90 173.75 89.11 Grey
91 170.31 85.81 Grey
92 168.86 95.05 Green
93 163.84 68.41 Blue
94 177.13 61.98 Grey
95 163.91 80.01 Brown
96 163.38 79.99 Green
97 176.37 71.59 Green
98 169.32 80.25 Blue
99 171.38 68.90 Green
100 169.38 74.83 Brown
101 159.26 68.96 Blue
102 175.53 97.56 Brown
103 167.83 92.94 Green
104 162.05 81.22 Brown
105 175.16 106.42 Grey
106 180.76 77.06 Green
107 173.87 92.64 Green
108 174.65 87.64 Blue
109 162.87 71.05 Grey
110 162.27 81.45 Green
111 158.18 92.18 Blue
112 169.17 88.93 Blue
113 164.27 71.72 Grey
114 178.32 98.51 Green
115 172.85 89.73 Grey
116 171.98 68.07 Blue
117 170.44 77.68 Brown
118 180.69 62.29 Blue
119 173.25 76.62 Blue
120 177.39 81.99 Brown
121 175.96 83.15 Grey
122 168.64 83.43 Blue
123 172.87 69.10 Blue
124 174.24 74.36 Green
125 163.52 89.09 Blue
126 173.86 91.25 Grey
127 166.18 75.99 Green
128 167.58 87.40 Grey
129 177.98 66.90 Green
130 168.78 95.97 Brown
131 166.73 80.93 Grey
132 169.20 81.77 Blue
133 181.24 53.61 Blue
134 167.48 78.43 Grey
135 172.15 77.08 Green
136 164.70 74.33 Brown
137 172.92 78.59 Blue
138 165.45 86.66 Grey
139 174.56 79.11 Grey
140 177.11 80.03 Blue
141 173.38 82.32 Blue
142 168.58 86.63 Green
143 172.66 74.01 Brown
144 170.90 70.48 Blue
145 172.37 91.75 Brown
146 167.83 69.16 Brown
147 171.23 93.25 Green
148 175.01 75.93 Brown
149 166.59 89.26 Grey
150 167.33 87.21 Brown
151 174.70 69.49 Grey
152 172.84 84.74 Blue
153 177.57 93.33 Green
154 157.15 87.62 Blue
155 175.08 89.77 Blue
156 160.76 83.96 Grey
157 165.28 71.93 Green
158 164.66 73.98 Blue
159 167.43 62.94 Green
160 167.03 78.37 Blue
161 171.62 77.27 Grey
162 178.03 78.77 Green
163 171.34 90.43 Brown
164 170.92 71.89 Green
165 170.69 71.62 Green
166 157.21 74.83 Brown
167 172.52 88.71 Brown
168 168.89 75.06 Blue
169 154.20 73.77 Green
170 168.11 79.51 Blue
171 165.75 82.18 Grey
172 177.43 78.84 Blue
173 161.59 56.02 Blue
174 168.76 80.26 Grey
175 178.73 85.63 Grey
176 159.83 77.43 Blue
177 161.85 79.72 Grey
178 164.47 86.25 Brown
179 168.78 87.44 Blue
180 168.74 76.94 Brown
181 174.76 76.40 Blue
182 158.93 62.92 Grey
183 184.02 75.70 Brown
184 180.14 85.63 Green
185 172.54 79.51 Green
186 177.91 79.62 Green
187 168.45 91.46 Blue
188 167.30 63.11 Green
189 179.36 85.37 Green
190 169.88 75.82 Green
191 172.71 71.37 Grey
192 175.90 76.31 Green
193 166.21 73.58 Grey
194 181.55 79.35 Brown
195 170.41 94.14 Brown
196 156.24 85.25 Green
197 167.50 83.20 Brown
198 168.21 92.82 Green
199 171.84 75.34 Grey
200 166.94 72.62 Brown
201 174.75 97.50 Blue
202 181.72 91.31 Grey
203 176.95 73.23 Grey
204 167.05 75.51 Grey
205 177.24 81.59 Green
206 169.89 82.19 Grey
207 177.97 73.41 Green
208 172.92 87.74 Green
209 175.05 72.68 Brown
210 175.71 76.34 Green
211 169.09 70.88 Blue
212 179.56 63.22 Blue
213 177.95 79.38 Brown
214 168.45 97.59 Green
215 170.22 60.53 Green
216 168.83 67.90 Green
217 168.85 73.84 Brown
218 173.56 84.11 Grey
219 171.26 80.39 Brown
220 173.70 106.24 Grey
221 171.59 78.38 Brown
222 171.65 97.62 Brown
223 180.83 76.16 Green
224 176.10 74.79 Brown
225 162.26 91.70 Green
226 167.96 72.58 Green
227 150.49 77.64 Grey
228 174.36 84.26 Green
229 164.27 88.67 Blue
230 171.19 72.31 Blue
231 161.76 81.70 Brown
232 164.25 85.40 Grey
233 162.72 72.36 Green
234 166.91 74.51 Grey
235 179.76 71.64 Blue
236 174.45 67.82 Grey
237 178.76 96.95 Blue
238 168.00 76.59 Blue
239 179.66 71.96 Grey
240 174.31 63.95 Blue
241 171.84 78.73 Brown
242 172.44 99.57 Green
243 163.48 79.66 Grey
244 166.40 65.72 Green
245 181.44 80.12 Blue
246 170.07 78.10 Brown
247 165.13 77.83 Blue
248 170.03 98.61 Brown
249 163.01 96.87 Grey
250 155.67 85.27 Green
251 161.81 84.74 Grey
252 177.27 81.66 Green
253 178.89 80.84 Grey
254 182.34 79.56 Blue
255 181.45 63.90 Blue
256 172.16 88.92 Brown
257 173.10 79.23 Grey
258 181.61 87.54 Brown
259 179.78 66.92 Blue
260 174.24 79.67 Green
261 162.32 96.22 Blue
262 171.49 93.26 Brown
263 175.61 74.34 Grey
264 167.38 78.83 Blue
265 180.99 72.20 Brown
266 178.88 92.41 Grey
267 168.14 77.18 Brown
268 167.75 93.80 Green
269 172.72 75.35 Green
270 174.72 85.31 Blue
271 172.84 97.59 Grey
272 162.77 78.83 Blue
273 170.30 88.87 Green
274 177.24 73.07 Green
275 166.88 91.85 Brown
276 167.67 76.55 Blue
277 171.28 85.02 Blue
278 170.17 87.99 Blue
279 167.41 69.63 Brown
280 169.73 75.10 Green
281 168.23 83.41 Grey
282 169.56 74.34 Green
283 172.44 67.44 Green
284 180.55 86.91 Grey
285 169.62 78.63 Blue
286 177.60 96.33 Blue
287 160.69 74.49 Brown
288 164.96 63.92 Grey
289 167.15 86.17 Brown
290 172.75 80.83 Green
291 164.50 88.16 Brown
292 175.62 85.31 Green
293 164.62 72.17 Green
294 175.26 89.28 Brown
295 161.04 73.38 Grey
296 160.15 81.88 Blue
297 172.63 74.39 Grey
298 170.20 92.62 Brown
299 177.24 102.26 Brown
300 173.70 79.81 Green
301 175.54 94.45 Blue
302 174.25 92.72 Green
303 184.04 94.57 Brown
304 178.58 77.41 Blue
305 176.58 83.59 Grey
306 176.23 67.81 Grey
307 184.50 77.26 Grey
308 173.22 79.99 Grey
309 174.17 71.37 Blue
310 164.35 75.98 Grey
311 171.74 76.68 Green
312 175.64 71.55 Brown
313 180.35 75.89 Brown
314 165.27 74.56 Brown
315 167.47 67.70 Brown
316 169.11 78.53 Grey
317 175.97 80.22 Brown
318 162.54 78.08 Blue
319 170.80 79.26 Blue
320 171.81 97.78 Grey
321 172.70 70.38 Blue
322 177.85 73.33 Blue
323 155.74 81.77 Grey
324 170.91 84.42 Blue
325 175.76 69.08 Brown
326 173.52 63.42 Blue
327 165.77 77.70 Brown
328 173.10 80.32 Blue
329 160.31 78.51 Green
330 172.25 70.85 Blue
331 170.17 91.80 Brown
332 175.93 89.74 Brown
333 158.50 82.41 Grey
334 163.55 69.42 Grey
335 169.81 75.71 Green
336 174.25 92.71 Brown
337 163.96 74.37 Blue
338 163.39 76.83 Green
339 168.58 72.02 Grey
340 158.66 70.04 Green
341 175.02 89.43 Green
342 178.57 92.62 Green
343 167.82 75.19 Blue
344 166.88 80.29 Green
345 172.10 80.81 Brown
346 174.20 73.98 Grey
347 171.52 98.77 Brown
348 156.98 74.24 Grey
349 163.02 85.50 Grey
350 167.81 77.21 Green
351 169.70 93.46 Grey
352 174.72 70.28 Green
353 174.00 60.69 Green
354 170.03 67.09 Brown
355 172.79 82.48 Green
356 168.03 77.84 Brown
357 178.78 98.07 Green
358 172.99 91.59 Blue
359 175.84 78.73 Grey
360 158.33 79.21 Brown
361 174.64 67.22 Grey
362 161.70 64.57 Green
363 180.42 65.96 Green
364 163.87 105.01 Blue
365 173.52 71.91 Grey
366 156.13 87.33 Blue
367 175.51 56.87 Brown
368 174.88 81.92 Brown
369 175.23 67.28 Grey
370 167.84 85.77 Green
371 169.73 72.42 Grey
372 164.01 87.38 Grey
373 177.31 66.59 Green
374 167.33 91.17 Grey
375 169.25 93.05 Green
376 171.28 81.61 Grey
377 170.92 70.60 Grey
378 161.43 71.33 Blue
379 166.05 62.82 Green
380 151.20 73.15 Blue
381 167.62 80.36 Brown
382 166.10 96.90 Green
383 173.65 81.27 Green
384 158.62 94.71 Green
385 175.73 86.82 Blue
386 166.44 82.27 Green
387 174.38 60.87 Blue
388 163.13 81.07 Grey
389 167.77 67.97 Grey
390 166.62 82.88 Blue
391 163.69 74.08 Green
392 172.64 74.28 Green
393 178.73 83.33 Green
394 173.00 80.02 Blue
395 178.43 73.85 Grey
396 173.80 85.39 Grey
397 168.28 76.13 Blue
398 167.18 88.48 Brown
399 167.99 75.53 Brown
400 171.02 79.73 Brown
401 172.28 85.47 Green
402 171.49 80.59 Brown
403 165.50 72.46 Grey
404 177.79 82.61 Brown
405 173.53 85.79 Blue
406 171.41 83.66 Green
407 161.80 60.30 Blue
408 152.92 82.55 Blue
409 170.02 83.78 Grey
410 172.42 91.13 Grey
411 164.93 62.11 Green
412 183.56 88.33 Brown
413 174.70 88.68 Blue
414 162.23 64.36 Green
415 182.68 86.08 Brown
416 165.07 83.41 Brown
417 161.78 76.40 Brown
418 163.44 61.74 Blue
419 164.02 102.66 Grey
420 170.30 95.17 Blue
421 168.91 73.51 Grey
422 167.68 79.19 Blue
423 175.17 63.84 Brown
424 158.61 86.90 Grey
425 160.16 71.20 Grey
426 173.88 110.85 Green
427 160.02 66.60 Blue
428 175.65 76.41 Brown
429 158.39 84.46 Brown
430 174.64 64.57 Brown
431 162.43 90.14 Grey
432 166.79 86.35 Brown
433 166.54 70.91 Grey
434 181.04 88.59 Green
435 162.29 85.64 Blue
436 166.36 83.70 Green
437 175.48 85.34 Blue
438 165.91 80.92 Green
439 171.30 84.06 Grey
440 160.78 83.18 Grey
441 178.63 76.45 Green
442 170.41 81.38 Blue
443 177.17 85.74 Green
444 167.45 96.81 Brown
445 159.95 67.26 Grey
446 166.89 78.03 Brown
447 160.71 65.79 Green
448 173.51 96.46 Green
449 166.79 74.44 Blue
450 170.98 87.59 Brown
451 158.55 75.68 Green
452 172.49 86.38 Green
453 167.15 95.10 Brown
454 166.62 74.01 Green
455 173.69 66.24 Brown
456 165.80 85.46 Grey
457 161.68 82.30 Blue
458 164.83 75.65 Green
459 172.23 79.47 Green
460 165.45 82.25 Green
461 167.30 80.58 Grey
462 181.39 83.28 Brown
463 170.32 69.53 Brown
464 167.47 78.83 Green
465 172.62 66.83 Brown
466 172.73 85.80 Brown
467 158.87 73.64 Grey
468 173.91 77.61 Grey
469 173.79 78.66 Blue
470 160.69 81.52 Green
471 175.99 87.79 Green
472 185.41 72.84 Green
473 170.41 70.52 Blue
474 168.41 87.86 Brown
475 178.33 75.76 Brown
476 170.63 89.72 Brown
477 155.62 71.01 Green
478 180.64 76.75 Grey
479 165.08 83.08 Grey
480 160.47 68.85 Brown
481 165.44 74.63 Grey
482 158.29 101.64 Grey
483 174.56 75.27 Grey
484 168.55 82.76 Green
485 173.77 83.34 Brown
486 172.73 76.19 Blue
487 162.55 65.94 Brown
488 180.66 93.36 Grey
489 170.04 83.57 Grey
490 174.42 80.01 Grey
491 173.36 88.68 Grey
492 167.22 93.74 Brown
493 178.84 91.50 Blue
494 173.05 90.13 Grey
495 162.47 80.31 Grey
496 177.18 81.62 Green
497 170.52 89.10 Blue
498 177.94 63.94 Grey
499 173.57 74.72 Brown
500 167.96 83.24 Brown
501 163.22 84.51 Brown
502 172.34 80.34 Green
503 168.71 62.97 Green
504 167.06 85.37 Brown
505 179.45 83.44 Green
506 166.20 91.28 Grey
507 159.74 69.81 Green
508 167.38 76.58 Brown
509 173.26 80.06 Blue
510 172.80 74.81 Brown
511 168.47 79.31 Brown
512 168.65 71.22 Grey
513 168.29 75.49 Brown
514 176.30 91.21 Green
515 168.88 57.29 Grey
516 169.84 90.20 Green
517 162.16 79.74 Brown
518 170.81 47.17 Grey
519 181.13 89.54 Grey
520 184.31 108.73 Blue
521 168.26 73.86 Grey
522 165.63 91.33 Grey
523 176.27 69.51 Green
524 167.91 77.48 Blue
525 171.15 70.10 Brown
526 168.91 76.16 Blue
527 158.62 88.97 Green
528 165.49 78.43 Grey
529 161.70 76.32 Green
530 169.87 80.65 Green
531 169.24 68.92 Grey
532 167.44 81.36 Blue
533 170.28 93.26 Green
534 166.24 51.22 Brown
535 173.13 96.14 Blue
536 179.70 81.85 Blue
537 163.47 63.42 Brown
538 169.36 75.30 Brown
539 174.58 76.04 Brown
540 175.88 79.06 Blue
541 167.46 78.88 Green
542 173.78 60.94 Grey
543 179.62 73.93 Blue
544 178.61 86.27 Green
545 169.03 73.02 Grey
546 165.26 83.74 Blue
547 164.43 81.78 Blue
548 161.73 87.55 Blue
549 171.62 73.66 Green
550 176.46 88.36 Grey
551 165.81 78.63 Grey
552 162.94 80.49 Brown
553 171.88 85.12 Blue
554 176.82 87.21 Grey
555 164.31 86.92 Brown
556 171.85 86.95 Brown
557 162.26 86.78 Green
558 173.73 74.23 Grey
559 176.51 88.45 Green
560 176.35 62.95 Brown
561 169.76 78.65 Grey
562 174.69 78.80 Grey
563 162.81 84.49 Grey
564 169.89 85.22 Green
565 163.11 78.19 Green
566 167.19 86.21 Brown
567 174.35 80.57 Green
568 153.12 82.01 Brown
569 157.22 83.38 Green
570 162.83 71.56 Blue
571 173.47 79.72 Brown
572 167.53 76.30 Blue
573 170.45 81.24 Green
574 163.47 87.96 Grey
575 179.40 92.09 Blue
576 167.31 65.00 Grey
577 169.58 69.80 Grey
578 168.05 85.77 Green
579 171.20 94.22 Green
580 176.27 90.02 Green
581 176.86 67.13 Grey
582 167.87 85.63 Grey
583 171.54 88.16 Blue
584 178.07 65.38 Blue
585 176.18 84.41 Blue
586 169.12 82.13 Green
587 172.05 81.30 Blue
588 163.15 84.83 Green
589 162.23 59.97 Green
590 168.35 73.77 Brown
591 171.76 73.92 Brown
592 172.66 101.87 Grey
593 159.81 93.57 Grey
594 169.99 99.69 Blue
595 174.63 55.19 Grey
596 165.59 79.99 Green
597 162.84 76.90 Brown
598 175.13 69.66 Grey
599 165.10 80.14 Brown
600 165.03 66.08 Grey
601 172.42 82.01 Brown
602 170.90 52.92 Green
603 178.50 85.73 Blue
604 172.34 68.28 Green
605 164.19 75.74 Brown
606 170.27 63.26 Blue
607 179.86 70.02 Green
608 166.47 96.09 Grey
609 169.49 75.83 Brown
610 166.44 91.30 Blue
611 155.93 66.45 Brown
612 173.59 78.59 Green
613 163.59 75.70 Green
614 180.90 92.72 Blue
615 173.41 86.40 Brown
616 176.83 89.82 Blue
617 175.75 68.52 Blue
618 164.01 70.47 Grey
619 166.44 82.43 Brown
620 171.51 70.19 Blue
621 169.78 77.99 Green
622 169.07 76.27 Brown
623 165.28 98.21 Brown
624 163.18 70.05 Grey
625 178.65 94.49 Green
626 177.72 58.70 Grey
627 176.59 82.13 Blue
628 169.60 71.51 Green
629 176.29 82.04 Grey
630 173.98 80.69 Green
631 174.35 80.32 Green
632 173.15 64.97 Grey
633 175.28 73.25 Green
634 167.41 67.19 Brown
635 164.19 89.81 Brown
636 183.06 93.59 Blue
637 175.10 78.25 Grey
638 176.74 74.15 Grey
639 178.84 92.62 Brown
640 175.70 70.23 Grey
641 164.96 75.14 Blue
642 161.02 78.67 Blue
643 176.35 77.17 Green
644 172.10 75.25 Grey
645 167.37 69.22 Grey
646 164.82 81.66 Blue
647 175.77 85.56 Blue
648 170.40 75.69 Green
649 173.13 64.69 Blue
650 169.66 65.95 Grey
651 169.40 70.44 Grey
652 180.18 76.36 Brown
653 166.35 84.95 Green
654 172.43 85.69 Blue
655 169.50 84.78 Blue
656 166.27 97.93 Grey
657 176.14 75.50 Green
658 170.92 93.58 Brown
659 171.55 82.20 Green
660 160.68 83.51 Blue
661 175.81 99.97 Blue
662 164.27 63.70 Blue
663 171.16 75.64 Blue
664 156.65 77.83 Brown
665 164.42 96.20 Green
666 175.12 84.65 Blue
667 165.84 45.42 Blue
668 182.88 89.95 Grey
669 178.37 72.67 Green
670 168.80 84.44 Green
671 179.85 86.00 Blue
672 174.85 100.53 Grey
673 172.78 80.65 Brown
674 180.36 73.94 Green
675 165.82 77.46 Grey
676 170.78 89.13 Blue
677 168.49 76.72 Brown
678 169.85 86.73 Blue
679 174.11 92.55 Green
680 170.83 97.03 Grey
681 179.09 76.15 Brown
682 166.33 87.17 Brown
683 164.41 68.12 Green
684 170.39 74.14 Grey
685 162.43 87.17 Grey
686 169.02 74.69 Blue
687 166.88 78.84 Brown
688 175.61 68.40 Brown
689 175.12 71.64 Blue
690 173.44 63.26 Grey
691 173.33 77.60 Brown
692 173.13 74.93 Brown
693 167.55 86.02 Brown
694 173.30 81.53 Blue
695 173.53 82.49 Blue
696 172.86 74.11 Grey
697 171.34 54.11 Grey
698 174.93 60.05 Grey
699 168.74 86.94 Green
700 172.22 91.44 Green
701 161.10 78.92 Grey
702 169.96 90.92 Brown
703 181.15 75.33 Grey
704 172.05 80.74 Brown
705 178.06 87.39 Brown
706 158.88 73.42 Blue
707 169.57 85.41 Grey
708 168.34 91.51 Brown
709 166.92 104.46 Grey
710 162.76 76.71 Grey
711 164.92 88.80 Green
712 172.33 66.96 Green
713 170.21 83.83 Brown
714 175.88 66.19 Brown
715 175.74 78.63 Grey
716 175.06 84.60 Brown
717 170.22 82.79 Grey
718 163.41 72.84 Brown
719 167.81 69.18 Brown
720 170.05 70.25 Brown
721 161.73 57.69 Blue
722 187.40 80.36 Blue
723 178.57 84.51 Green
724 168.97 84.38 Grey
725 176.59 77.63 Brown
726 168.18 74.67 Brown
727 179.48 64.46 Brown
728 161.75 95.80 Grey
729 168.11 76.98 Brown
730 174.14 80.32 Green
731 164.47 90.74 Brown
732 160.48 68.74 Brown
733 165.24 65.82 Green
734 179.93 76.49 Grey
735 169.37 65.14 Blue
736 177.01 82.25 Blue
737 171.66 89.68 Grey
738 161.98 83.14 Blue
739 182.92 68.73 Grey
740 175.51 77.38 Green
741 165.45 94.28 Green
742 175.55 89.13 Grey
743 171.25 81.51 Grey
744 173.31 81.15 Grey
745 169.20 83.91 Blue
746 176.58 64.95 Brown
747 177.51 58.00 Brown
748 157.56 72.30 Green
749 180.94 88.69 Green
750 160.33 89.71 Green
751 172.03 75.78 Blue
752 177.04 82.96 Blue
753 169.15 71.61 Green
754 165.06 69.66 Grey
755 170.48 93.27 Grey
756 165.01 77.70 Grey
757 171.92 65.34 Brown
758 170.18 68.41 Green
759 164.87 81.80 Grey
760 168.39 87.68 Grey
761 162.04 77.53 Brown
762 177.38 90.14 Brown
763 176.05 82.96 Green
764 185.33 97.28 Green
765 172.98 87.51 Brown
766 174.89 68.85 Grey
767 174.46 76.35 Grey
768 171.37 68.31 Grey
769 171.27 94.03 Green
770 168.07 90.74 Brown
771 174.33 57.42 Brown
772 174.21 80.50 Green
773 167.70 66.39 Green
774 164.26 80.39 Grey
775 186.83 79.01 Brown
776 174.32 83.73 Grey
777 173.50 92.93 Brown
778 169.33 69.16 Green
779 176.49 67.70 Grey
780 170.68 85.13 Green
781 169.74 67.86 Grey
782 162.16 91.99 Green
783 175.25 87.20 Green
784 182.75 79.18 Grey
785 170.20 59.65 Green
786 164.19 88.33 Green
787 163.85 91.10 Green
788 164.92 82.03 Brown
789 178.15 85.93 Grey
790 163.24 88.94 Brown
791 165.46 86.33 Blue
792 172.60 83.24 Brown
793 167.47 81.87 Brown
794 171.98 91.66 Green
795 179.25 69.31 Grey
796 172.06 74.56 Brown
797 166.93 78.48 Grey
798 172.85 63.76 Grey
799 165.20 78.90 Grey
800 179.49 88.48 Blue
801 174.78 65.54 Blue
802 168.69 70.52 Brown
803 180.63 82.52 Blue
804 172.99 100.94 Green
805 165.76 67.77 Green
806 166.49 82.86 Blue
807 169.43 57.92 Brown
808 171.73 81.76 Green
809 163.62 88.36 Blue
810 159.71 86.31 Green
811 182.76 82.51 Brown
812 161.47 72.81 Brown
813 173.19 75.70 Green
814 163.44 86.56 Brown
815 176.67 60.29 Blue
816 163.43 97.09 Grey
817 173.28 76.30 Green
818 172.58 83.69 Grey
819 164.32 77.01 Brown
820 168.22 67.88 Blue
821 150.92 77.64 Brown
822 172.76 80.55 Blue
823 164.35 73.69 Green
824 165.69 75.06 Grey
825 176.16 84.56 Grey
826 157.74 88.40 Green
827 170.35 76.74 Green
828 183.95 80.39 Blue
829 162.00 78.95 Blue
830 181.28 66.60 Green
831 174.39 56.65 Grey
832 159.20 86.40 Grey
833 174.50 65.25 Brown
834 163.03 80.33 Blue
835 167.41 80.36 Brown
836 165.03 89.11 Grey
837 179.04 87.35 Blue
838 161.36 78.58 Green
839 166.11 68.33 Brown
840 168.41 71.24 Green
841 171.07 85.61 Grey
842 175.04 61.38 Grey
843 174.98 68.79 Brown
844 164.68 86.80 Green
845 166.59 82.69 Brown
846 159.65 74.14 Brown
847 179.09 91.54 Green
848 164.22 78.42 Green
849 164.55 85.67 Grey
850 182.11 92.52 Green
851 174.90 93.75 Green
852 172.54 88.82 Blue
853 170.84 77.66 Blue
854 175.22 68.17 Blue
855 175.12 71.78 Blue
856 162.62 89.11 Blue
857 170.29 79.53 Brown
858 174.84 61.45 Grey
859 173.65 82.97 Green
860 164.60 86.46 Green
861 178.36 54.60 Green
862 164.19 83.58 Blue
863 157.51 82.66 Brown
864 174.13 76.87 Brown
865 165.17 64.90 Green
866 177.45 63.20 Brown
867 167.33 74.84 Grey
868 175.80 81.74 Green
869 172.49 81.38 Green
870 162.09 78.26 Green
871 173.98 78.24 Grey
872 171.09 74.43 Blue
873 167.84 69.64 Green
874 168.60 70.73 Blue
875 163.46 81.89 Blue
876 177.19 79.26 Blue
877 161.45 58.22 Grey
878 174.31 69.15 Grey
879 172.42 72.58 Brown
880 167.85 80.45 Grey
881 168.74 99.20 Green
882 165.86 80.97 Brown
883 169.62 70.98 Green
884 167.87 84.41 Green
885 165.95 98.69 Blue
886 155.84 79.45 Grey
887 171.42 78.69 Blue
888 171.14 106.46 Blue
889 168.84 88.28 Green
890 175.91 66.87 Green
891 175.18 81.04 Grey
892 171.30 80.72 Blue
893 165.17 71.09 Grey
894 178.78 88.12 Green
895 174.62 71.12 Grey
896 170.26 68.25 Green
897 179.31 58.19 Green
898 180.51 96.41 Blue
899 173.53 92.05 Brown
900 165.74 76.31 Grey
901 176.17 87.32 Brown
902 167.82 88.80 Brown
903 164.41 85.48 Green
904 161.65 87.52 Grey
905 163.57 90.17 Grey
906 163.10 90.68 Green
907 170.69 87.38 Grey
908 167.90 84.00 Green
909 174.47 80.93 Green
910 172.46 93.12 Green
911 169.07 65.93 Grey
912 171.98 77.01 Grey
913 166.94 75.92 Green
914 168.10 73.89 Green
915 168.69 74.37 Blue
916 174.00 77.32 Brown
917 156.31 75.34 Brown
918 155.59 81.60 Green
919 162.65 80.18 Grey
920 163.22 84.07 Green
921 166.35 80.21 Brown
922 173.69 72.18 Brown
923 177.07 54.74 Green
924 186.69 61.83 Blue
925 167.84 68.31 Blue
926 162.95 83.75 Grey
927 170.66 65.66 Grey
928 169.88 71.46 Green
929 173.43 69.61 Brown
930 165.00 77.79 Blue
931 174.13 90.35 Brown
932 171.46 73.28 Brown
933 164.49 82.80 Green
934 152.30 75.36 Green
935 174.43 87.18 Blue
936 165.58 102.13 Blue
937 160.29 77.79 Green
938 170.25 86.01 Grey
939 177.55 91.71 Grey
940 164.84 94.45 Blue
941 164.07 79.20 Green
942 166.57 84.99 Blue
943 161.47 97.52 Grey
944 173.55 85.37 Blue
945 163.59 81.39 Grey
946 162.13 76.12 Blue
947 163.10 88.56 Blue
948 170.11 57.10 Green
949 166.96 79.89 Grey
950 172.18 77.77 Grey
951 165.04 74.91 Blue
952 169.23 82.95 Blue
953 170.65 69.72 Blue
954 173.66 76.40 Brown
955 162.64 65.73 Brown
956 163.84 80.17 Brown
957 163.12 102.35 Blue
958 163.57 82.56 Brown
959 169.02 75.04 Green
960 176.90 62.60 Brown
961 164.87 73.71 Green
962 183.08 79.86 Brown
963 175.47 80.01 Blue
964 168.96 77.69 Grey
965 167.64 87.86 Green
966 175.09 75.73 Blue
967 166.50 82.40 Brown
968 181.62 79.34 Green
969 183.81 67.89 Grey
970 182.15 80.46 Green
971 166.94 87.38 Blue
972 172.27 110.86 Blue
973 168.78 62.85 Green
974 159.33 84.94 Brown
975 169.17 90.67 Brown
976 159.78 106.06 Blue
977 169.47 88.83 Green
978 168.82 92.05 Grey
979 169.06 74.83 Blue
980 174.91 70.33 Green
981 176.09 81.09 Green
982 162.05 86.69 Blue
983 168.60 76.24 Green
984 171.85 80.32 Green
985 168.91 89.18 Green
986 170.05 89.86 Brown
987 163.26 80.00 Brown
988 174.87 90.83 Brown
989 163.92 83.57 Blue
990 166.18 85.91 Grey
991 180.81 68.73 Grey
992 171.91 90.01 Green
993 176.89 76.97 Blue
994 174.08 59.10 Blue
995 156.06 102.07 Green
996 163.94 85.15 Grey
997 161.96 68.63 Blue
998 169.91 81.64 Brown
999 165.87 71.79 Grey
1000 156.67 86.92 Grey

Random assignment

I’m now going to flip (an imaginary, computer-generated) coin for each of these 1,000 individuals to assigned them to group A or B:

ID Height Weight Eye colour Group
1 164.26 52.92 Green A
2 166.89 84.08 Grey B
3 173.48 76.97 Brown A
4 170.48 84.42 Blue A
5 175.38 86.80 Green A
6 167.74 73.26 Blue B
7 176.89 78.91 Blue B
8 170.59 86.85 Brown A
9 176.90 84.77 Blue A
10 171.01 69.88 Grey A
11 168.57 71.46 Blue B
12 170.08 83.52 Green B
13 169.57 69.79 Grey B
14 168.58 74.14 Grey A
15 167.81 75.07 Grey A
16 171.51 60.62 Brown B
17 170.24 60.93 Brown B
18 171.78 74.47 Grey B
19 180.18 93.82 Blue A
20 173.31 83.43 Green A
21 161.92 99.96 Grey A
22 173.14 74.92 Green A
23 175.69 79.47 Brown A
24 181.84 94.84 Green B
25 165.85 91.22 Grey B
26 168.48 76.40 Green B
27 178.39 68.96 Grey B
28 174.01 83.72 Brown B
29 181.95 78.79 Brown B
30 171.50 73.69 Blue A
31 158.98 88.57 Green B
32 175.80 82.91 Grey B
33 177.61 62.68 Green A
34 170.61 66.02 Blue A
35 165.31 70.63 Blue B
36 171.15 65.33 Brown B
37 175.04 88.20 Grey A
38 172.63 66.92 Grey A
39 174.24 77.46 Grey B
40 171.23 72.70 Green B
41 181.85 76.38 Brown B
42 169.84 72.25 Brown B
43 178.83 86.12 Grey B
44 180.32 69.69 Brown B
45 168.65 72.67 Green A
46 162.35 57.10 Blue B
47 152.79 78.98 Grey A
48 172.59 83.20 Green A
49 173.95 75.92 Blue B
50 175.94 90.79 Green B
51 167.77 68.77 Green B
52 164.13 70.63 Blue A
53 175.30 75.30 Grey B
54 168.81 88.19 Green A
55 167.47 83.78 Brown A
56 168.07 74.57 Blue B
57 157.69 60.87 Blue B
58 164.92 74.49 Brown B
59 171.48 75.50 Brown B
60 157.84 79.47 Green B
61 174.07 86.33 Brown B
62 161.46 70.05 Grey A
63 170.23 80.54 Blue A
64 170.85 90.98 Grey A
65 178.94 74.48 Grey B
66 173.93 64.49 Blue A
67 173.22 67.79 Brown A
68 175.84 71.85 Blue A
69 170.90 93.90 Green B
70 160.68 69.41 Blue B
71 171.09 79.61 Blue A
72 180.43 79.34 Green A
73 163.23 107.84 Brown A
74 163.43 72.68 Grey B
75 166.36 92.99 Green B
76 168.49 91.05 Brown B
77 174.75 84.66 Grey B
78 162.17 91.25 Brown B
79 166.22 93.94 Blue A
80 164.78 89.26 Green B
81 169.83 67.22 Blue B
82 166.89 67.41 Grey B
83 167.84 71.53 Grey A
84 170.30 64.05 Brown A
85 179.13 72.42 Green B
86 161.91 71.91 Brown B
87 180.92 85.47 Grey A
88 168.68 63.92 Green B
89 176.12 77.45 Brown B
90 173.75 89.11 Grey A
91 170.31 85.81 Grey A
92 168.86 95.05 Green A
93 163.84 68.41 Blue B
94 177.13 61.98 Grey A
95 163.91 80.01 Brown B
96 163.38 79.99 Green B
97 176.37 71.59 Green B
98 169.32 80.25 Blue A
99 171.38 68.90 Green B
100 169.38 74.83 Brown A
101 159.26 68.96 Blue A
102 175.53 97.56 Brown B
103 167.83 92.94 Green A
104 162.05 81.22 Brown A
105 175.16 106.42 Grey A
106 180.76 77.06 Green A
107 173.87 92.64 Green B
108 174.65 87.64 Blue A
109 162.87 71.05 Grey B
110 162.27 81.45 Green B
111 158.18 92.18 Blue B
112 169.17 88.93 Blue B
113 164.27 71.72 Grey A
114 178.32 98.51 Green A
115 172.85 89.73 Grey A
116 171.98 68.07 Blue B
117 170.44 77.68 Brown B
118 180.69 62.29 Blue A
119 173.25 76.62 Blue A
120 177.39 81.99 Brown A
121 175.96 83.15 Grey B
122 168.64 83.43 Blue B
123 172.87 69.10 Blue A
124 174.24 74.36 Green B
125 163.52 89.09 Blue A
126 173.86 91.25 Grey A
127 166.18 75.99 Green A
128 167.58 87.40 Grey B
129 177.98 66.90 Green B
130 168.78 95.97 Brown A
131 166.73 80.93 Grey B
132 169.20 81.77 Blue B
133 181.24 53.61 Blue B
134 167.48 78.43 Grey A
135 172.15 77.08 Green A
136 164.70 74.33 Brown B
137 172.92 78.59 Blue A
138 165.45 86.66 Grey B
139 174.56 79.11 Grey A
140 177.11 80.03 Blue A
141 173.38 82.32 Blue A
142 168.58 86.63 Green A
143 172.66 74.01 Brown B
144 170.90 70.48 Blue A
145 172.37 91.75 Brown B
146 167.83 69.16 Brown B
147 171.23 93.25 Green A
148 175.01 75.93 Brown A
149 166.59 89.26 Grey B
150 167.33 87.21 Brown B
151 174.70 69.49 Grey B
152 172.84 84.74 Blue A
153 177.57 93.33 Green A
154 157.15 87.62 Blue B
155 175.08 89.77 Blue A
156 160.76 83.96 Grey A
157 165.28 71.93 Green B
158 164.66 73.98 Blue B
159 167.43 62.94 Green B
160 167.03 78.37 Blue B
161 171.62 77.27 Grey A
162 178.03 78.77 Green B
163 171.34 90.43 Brown B
164 170.92 71.89 Green B
165 170.69 71.62 Green B
166 157.21 74.83 Brown B
167 172.52 88.71 Brown A
168 168.89 75.06 Blue B
169 154.20 73.77 Green A
170 168.11 79.51 Blue B
171 165.75 82.18 Grey B
172 177.43 78.84 Blue B
173 161.59 56.02 Blue A
174 168.76 80.26 Grey A
175 178.73 85.63 Grey B
176 159.83 77.43 Blue A
177 161.85 79.72 Grey B
178 164.47 86.25 Brown B
179 168.78 87.44 Blue B
180 168.74 76.94 Brown B
181 174.76 76.40 Blue B
182 158.93 62.92 Grey B
183 184.02 75.70 Brown A
184 180.14 85.63 Green A
185 172.54 79.51 Green A
186 177.91 79.62 Green A
187 168.45 91.46 Blue B
188 167.30 63.11 Green A
189 179.36 85.37 Green B
190 169.88 75.82 Green B
191 172.71 71.37 Grey A
192 175.90 76.31 Green A
193 166.21 73.58 Grey A
194 181.55 79.35 Brown B
195 170.41 94.14 Brown B
196 156.24 85.25 Green A
197 167.50 83.20 Brown B
198 168.21 92.82 Green A
199 171.84 75.34 Grey A
200 166.94 72.62 Brown A
201 174.75 97.50 Blue B
202 181.72 91.31 Grey A
203 176.95 73.23 Grey B
204 167.05 75.51 Grey A
205 177.24 81.59 Green B
206 169.89 82.19 Grey B
207 177.97 73.41 Green B
208 172.92 87.74 Green B
209 175.05 72.68 Brown B
210 175.71 76.34 Green B
211 169.09 70.88 Blue A
212 179.56 63.22 Blue B
213 177.95 79.38 Brown B
214 168.45 97.59 Green A
215 170.22 60.53 Green A
216 168.83 67.90 Green A
217 168.85 73.84 Brown B
218 173.56 84.11 Grey B
219 171.26 80.39 Brown B
220 173.70 106.24 Grey A
221 171.59 78.38 Brown A
222 171.65 97.62 Brown A
223 180.83 76.16 Green B
224 176.10 74.79 Brown A
225 162.26 91.70 Green B
226 167.96 72.58 Green B
227 150.49 77.64 Grey A
228 174.36 84.26 Green B
229 164.27 88.67 Blue A
230 171.19 72.31 Blue A
231 161.76 81.70 Brown B
232 164.25 85.40 Grey B
233 162.72 72.36 Green A
234 166.91 74.51 Grey A
235 179.76 71.64 Blue B
236 174.45 67.82 Grey B
237 178.76 96.95 Blue B
238 168.00 76.59 Blue A
239 179.66 71.96 Grey A
240 174.31 63.95 Blue A
241 171.84 78.73 Brown A
242 172.44 99.57 Green A
243 163.48 79.66 Grey A
244 166.40 65.72 Green B
245 181.44 80.12 Blue A
246 170.07 78.10 Brown A
247 165.13 77.83 Blue B
248 170.03 98.61 Brown A
249 163.01 96.87 Grey B
250 155.67 85.27 Green B
251 161.81 84.74 Grey A
252 177.27 81.66 Green A
253 178.89 80.84 Grey B
254 182.34 79.56 Blue A
255 181.45 63.90 Blue B
256 172.16 88.92 Brown B
257 173.10 79.23 Grey A
258 181.61 87.54 Brown B
259 179.78 66.92 Blue B
260 174.24 79.67 Green A
261 162.32 96.22 Blue A
262 171.49 93.26 Brown A
263 175.61 74.34 Grey B
264 167.38 78.83 Blue B
265 180.99 72.20 Brown A
266 178.88 92.41 Grey B
267 168.14 77.18 Brown A
268 167.75 93.80 Green B
269 172.72 75.35 Green B
270 174.72 85.31 Blue B
271 172.84 97.59 Grey A
272 162.77 78.83 Blue B
273 170.30 88.87 Green A
274 177.24 73.07 Green A
275 166.88 91.85 Brown A
276 167.67 76.55 Blue A
277 171.28 85.02 Blue A
278 170.17 87.99 Blue B
279 167.41 69.63 Brown A
280 169.73 75.10 Green B
281 168.23 83.41 Grey A
282 169.56 74.34 Green B
283 172.44 67.44 Green A
284 180.55 86.91 Grey B
285 169.62 78.63 Blue B
286 177.60 96.33 Blue A
287 160.69 74.49 Brown B
288 164.96 63.92 Grey A
289 167.15 86.17 Brown A
290 172.75 80.83 Green A
291 164.50 88.16 Brown B
292 175.62 85.31 Green B
293 164.62 72.17 Green B
294 175.26 89.28 Brown B
295 161.04 73.38 Grey B
296 160.15 81.88 Blue B
297 172.63 74.39 Grey A
298 170.20 92.62 Brown A
299 177.24 102.26 Brown B
300 173.70 79.81 Green B
301 175.54 94.45 Blue B
302 174.25 92.72 Green A
303 184.04 94.57 Brown B
304 178.58 77.41 Blue A
305 176.58 83.59 Grey B
306 176.23 67.81 Grey B
307 184.50 77.26 Grey A
308 173.22 79.99 Grey B
309 174.17 71.37 Blue B
310 164.35 75.98 Grey A
311 171.74 76.68 Green A
312 175.64 71.55 Brown B
313 180.35 75.89 Brown B
314 165.27 74.56 Brown A
315 167.47 67.70 Brown A
316 169.11 78.53 Grey A
317 175.97 80.22 Brown B
318 162.54 78.08 Blue B
319 170.80 79.26 Blue B
320 171.81 97.78 Grey A
321 172.70 70.38 Blue A
322 177.85 73.33 Blue B
323 155.74 81.77 Grey B
324 170.91 84.42 Blue A
325 175.76 69.08 Brown B
326 173.52 63.42 Blue A
327 165.77 77.70 Brown B
328 173.10 80.32 Blue B
329 160.31 78.51 Green A
330 172.25 70.85 Blue A
331 170.17 91.80 Brown A
332 175.93 89.74 Brown A
333 158.50 82.41 Grey B
334 163.55 69.42 Grey B
335 169.81 75.71 Green B
336 174.25 92.71 Brown B
337 163.96 74.37 Blue A
338 163.39 76.83 Green A
339 168.58 72.02 Grey A
340 158.66 70.04 Green A
341 175.02 89.43 Green A
342 178.57 92.62 Green A
343 167.82 75.19 Blue B
344 166.88 80.29 Green A
345 172.10 80.81 Brown B
346 174.20 73.98 Grey A
347 171.52 98.77 Brown B
348 156.98 74.24 Grey B
349 163.02 85.50 Grey B
350 167.81 77.21 Green A
351 169.70 93.46 Grey A
352 174.72 70.28 Green B
353 174.00 60.69 Green A
354 170.03 67.09 Brown B
355 172.79 82.48 Green A
356 168.03 77.84 Brown A
357 178.78 98.07 Green B
358 172.99 91.59 Blue A
359 175.84 78.73 Grey B
360 158.33 79.21 Brown B
361 174.64 67.22 Grey B
362 161.70 64.57 Green A
363 180.42 65.96 Green A
364 163.87 105.01 Blue A
365 173.52 71.91 Grey B
366 156.13 87.33 Blue A
367 175.51 56.87 Brown B
368 174.88 81.92 Brown B
369 175.23 67.28 Grey B
370 167.84 85.77 Green A
371 169.73 72.42 Grey B
372 164.01 87.38 Grey B
373 177.31 66.59 Green B
374 167.33 91.17 Grey A
375 169.25 93.05 Green B
376 171.28 81.61 Grey B
377 170.92 70.60 Grey A
378 161.43 71.33 Blue A
379 166.05 62.82 Green A
380 151.20 73.15 Blue B
381 167.62 80.36 Brown A
382 166.10 96.90 Green A
383 173.65 81.27 Green B
384 158.62 94.71 Green B
385 175.73 86.82 Blue B
386 166.44 82.27 Green B
387 174.38 60.87 Blue A
388 163.13 81.07 Grey B
389 167.77 67.97 Grey A
390 166.62 82.88 Blue B
391 163.69 74.08 Green A
392 172.64 74.28 Green A
393 178.73 83.33 Green B
394 173.00 80.02 Blue A
395 178.43 73.85 Grey B
396 173.80 85.39 Grey B
397 168.28 76.13 Blue B
398 167.18 88.48 Brown B
399 167.99 75.53 Brown B
400 171.02 79.73 Brown B
401 172.28 85.47 Green B
402 171.49 80.59 Brown B
403 165.50 72.46 Grey A
404 177.79 82.61 Brown B
405 173.53 85.79 Blue A
406 171.41 83.66 Green A
407 161.80 60.30 Blue B
408 152.92 82.55 Blue A
409 170.02 83.78 Grey A
410 172.42 91.13 Grey A
411 164.93 62.11 Green A
412 183.56 88.33 Brown A
413 174.70 88.68 Blue A
414 162.23 64.36 Green B
415 182.68 86.08 Brown B
416 165.07 83.41 Brown A
417 161.78 76.40 Brown B
418 163.44 61.74 Blue B
419 164.02 102.66 Grey B
420 170.30 95.17 Blue B
421 168.91 73.51 Grey B
422 167.68 79.19 Blue B
423 175.17 63.84 Brown B
424 158.61 86.90 Grey B
425 160.16 71.20 Grey B
426 173.88 110.85 Green A
427 160.02 66.60 Blue A
428 175.65 76.41 Brown A
429 158.39 84.46 Brown B
430 174.64 64.57 Brown B
431 162.43 90.14 Grey B
432 166.79 86.35 Brown A
433 166.54 70.91 Grey A
434 181.04 88.59 Green A
435 162.29 85.64 Blue A
436 166.36 83.70 Green B
437 175.48 85.34 Blue B
438 165.91 80.92 Green B
439 171.30 84.06 Grey A
440 160.78 83.18 Grey B
441 178.63 76.45 Green B
442 170.41 81.38 Blue A
443 177.17 85.74 Green B
444 167.45 96.81 Brown A
445 159.95 67.26 Grey B
446 166.89 78.03 Brown A
447 160.71 65.79 Green A
448 173.51 96.46 Green B
449 166.79 74.44 Blue A
450 170.98 87.59 Brown B
451 158.55 75.68 Green B
452 172.49 86.38 Green B
453 167.15 95.10 Brown A
454 166.62 74.01 Green B
455 173.69 66.24 Brown A
456 165.80 85.46 Grey A
457 161.68 82.30 Blue B
458 164.83 75.65 Green B
459 172.23 79.47 Green B
460 165.45 82.25 Green B
461 167.30 80.58 Grey A
462 181.39 83.28 Brown B
463 170.32 69.53 Brown B
464 167.47 78.83 Green B
465 172.62 66.83 Brown A
466 172.73 85.80 Brown B
467 158.87 73.64 Grey A
468 173.91 77.61 Grey B
469 173.79 78.66 Blue B
470 160.69 81.52 Green B
471 175.99 87.79 Green A
472 185.41 72.84 Green A
473 170.41 70.52 Blue B
474 168.41 87.86 Brown A
475 178.33 75.76 Brown A
476 170.63 89.72 Brown A
477 155.62 71.01 Green A
478 180.64 76.75 Grey A
479 165.08 83.08 Grey A
480 160.47 68.85 Brown A
481 165.44 74.63 Grey B
482 158.29 101.64 Grey B
483 174.56 75.27 Grey A
484 168.55 82.76 Green A
485 173.77 83.34 Brown B
486 172.73 76.19 Blue B
487 162.55 65.94 Brown B
488 180.66 93.36 Grey A
489 170.04 83.57 Grey A
490 174.42 80.01 Grey B
491 173.36 88.68 Grey B
492 167.22 93.74 Brown B
493 178.84 91.50 Blue A
494 173.05 90.13 Grey B
495 162.47 80.31 Grey A
496 177.18 81.62 Green B
497 170.52 89.10 Blue A
498 177.94 63.94 Grey A
499 173.57 74.72 Brown B
500 167.96 83.24 Brown A
501 163.22 84.51 Brown A
502 172.34 80.34 Green B
503 168.71 62.97 Green A
504 167.06 85.37 Brown B
505 179.45 83.44 Green A
506 166.20 91.28 Grey B
507 159.74 69.81 Green B
508 167.38 76.58 Brown B
509 173.26 80.06 Blue B
510 172.80 74.81 Brown B
511 168.47 79.31 Brown A
512 168.65 71.22 Grey B
513 168.29 75.49 Brown A
514 176.30 91.21 Green A
515 168.88 57.29 Grey B
516 169.84 90.20 Green B
517 162.16 79.74 Brown A
518 170.81 47.17 Grey B
519 181.13 89.54 Grey B
520 184.31 108.73 Blue B
521 168.26 73.86 Grey B
522 165.63 91.33 Grey A
523 176.27 69.51 Green A
524 167.91 77.48 Blue B
525 171.15 70.10 Brown A
526 168.91 76.16 Blue A
527 158.62 88.97 Green A
528 165.49 78.43 Grey B
529 161.70 76.32 Green B
530 169.87 80.65 Green B
531 169.24 68.92 Grey B
532 167.44 81.36 Blue A
533 170.28 93.26 Green A
534 166.24 51.22 Brown B
535 173.13 96.14 Blue B
536 179.70 81.85 Blue B
537 163.47 63.42 Brown A
538 169.36 75.30 Brown B
539 174.58 76.04 Brown A
540 175.88 79.06 Blue A
541 167.46 78.88 Green B
542 173.78 60.94 Grey A
543 179.62 73.93 Blue B
544 178.61 86.27 Green B
545 169.03 73.02 Grey A
546 165.26 83.74 Blue B
547 164.43 81.78 Blue A
548 161.73 87.55 Blue B
549 171.62 73.66 Green B
550 176.46 88.36 Grey B
551 165.81 78.63 Grey B
552 162.94 80.49 Brown B
553 171.88 85.12 Blue A
554 176.82 87.21 Grey B
555 164.31 86.92 Brown A
556 171.85 86.95 Brown B
557 162.26 86.78 Green A
558 173.73 74.23 Grey B
559 176.51 88.45 Green A
560 176.35 62.95 Brown A
561 169.76 78.65 Grey B
562 174.69 78.80 Grey A
563 162.81 84.49 Grey B
564 169.89 85.22 Green B
565 163.11 78.19 Green A
566 167.19 86.21 Brown B
567 174.35 80.57 Green A
568 153.12 82.01 Brown A
569 157.22 83.38 Green A
570 162.83 71.56 Blue A
571 173.47 79.72 Brown B
572 167.53 76.30 Blue A
573 170.45 81.24 Green A
574 163.47 87.96 Grey A
575 179.40 92.09 Blue A
576 167.31 65.00 Grey B
577 169.58 69.80 Grey B
578 168.05 85.77 Green A
579 171.20 94.22 Green B
580 176.27 90.02 Green B
581 176.86 67.13 Grey A
582 167.87 85.63 Grey A
583 171.54 88.16 Blue A
584 178.07 65.38 Blue A
585 176.18 84.41 Blue A
586 169.12 82.13 Green B
587 172.05 81.30 Blue B
588 163.15 84.83 Green B
589 162.23 59.97 Green A
590 168.35 73.77 Brown A
591 171.76 73.92 Brown A
592 172.66 101.87 Grey B
593 159.81 93.57 Grey A
594 169.99 99.69 Blue A
595 174.63 55.19 Grey A
596 165.59 79.99 Green B
597 162.84 76.90 Brown B
598 175.13 69.66 Grey A
599 165.10 80.14 Brown A
600 165.03 66.08 Grey A
601 172.42 82.01 Brown B
602 170.90 52.92 Green A
603 178.50 85.73 Blue B
604 172.34 68.28 Green B
605 164.19 75.74 Brown B
606 170.27 63.26 Blue B
607 179.86 70.02 Green A
608 166.47 96.09 Grey A
609 169.49 75.83 Brown A
610 166.44 91.30 Blue A
611 155.93 66.45 Brown B
612 173.59 78.59 Green A
613 163.59 75.70 Green A
614 180.90 92.72 Blue A
615 173.41 86.40 Brown A
616 176.83 89.82 Blue B
617 175.75 68.52 Blue A
618 164.01 70.47 Grey A
619 166.44 82.43 Brown A
620 171.51 70.19 Blue B
621 169.78 77.99 Green A
622 169.07 76.27 Brown B
623 165.28 98.21 Brown B
624 163.18 70.05 Grey B
625 178.65 94.49 Green B
626 177.72 58.70 Grey B
627 176.59 82.13 Blue A
628 169.60 71.51 Green B
629 176.29 82.04 Grey B
630 173.98 80.69 Green B
631 174.35 80.32 Green B
632 173.15 64.97 Grey A
633 175.28 73.25 Green A
634 167.41 67.19 Brown B
635 164.19 89.81 Brown B
636 183.06 93.59 Blue A
637 175.10 78.25 Grey B
638 176.74 74.15 Grey A
639 178.84 92.62 Brown A
640 175.70 70.23 Grey A
641 164.96 75.14 Blue A
642 161.02 78.67 Blue B
643 176.35 77.17 Green B
644 172.10 75.25 Grey A
645 167.37 69.22 Grey B
646 164.82 81.66 Blue A
647 175.77 85.56 Blue B
648 170.40 75.69 Green B
649 173.13 64.69 Blue A
650 169.66 65.95 Grey A
651 169.40 70.44 Grey A
652 180.18 76.36 Brown B
653 166.35 84.95 Green A
654 172.43 85.69 Blue A
655 169.50 84.78 Blue B
656 166.27 97.93 Grey A
657 176.14 75.50 Green A
658 170.92 93.58 Brown B
659 171.55 82.20 Green B
660 160.68 83.51 Blue A
661 175.81 99.97 Blue B
662 164.27 63.70 Blue A
663 171.16 75.64 Blue A
664 156.65 77.83 Brown B
665 164.42 96.20 Green A
666 175.12 84.65 Blue B
667 165.84 45.42 Blue B
668 182.88 89.95 Grey A
669 178.37 72.67 Green A
670 168.80 84.44 Green A
671 179.85 86.00 Blue B
672 174.85 100.53 Grey B
673 172.78 80.65 Brown B
674 180.36 73.94 Green A
675 165.82 77.46 Grey B
676 170.78 89.13 Blue A
677 168.49 76.72 Brown B
678 169.85 86.73 Blue B
679 174.11 92.55 Green B
680 170.83 97.03 Grey A
681 179.09 76.15 Brown B
682 166.33 87.17 Brown B
683 164.41 68.12 Green B
684 170.39 74.14 Grey A
685 162.43 87.17 Grey A
686 169.02 74.69 Blue A
687 166.88 78.84 Brown A
688 175.61 68.40 Brown B
689 175.12 71.64 Blue B
690 173.44 63.26 Grey A
691 173.33 77.60 Brown B
692 173.13 74.93 Brown B
693 167.55 86.02 Brown B
694 173.30 81.53 Blue B
695 173.53 82.49 Blue B
696 172.86 74.11 Grey A
697 171.34 54.11 Grey B
698 174.93 60.05 Grey B
699 168.74 86.94 Green B
700 172.22 91.44 Green B
701 161.10 78.92 Grey B
702 169.96 90.92 Brown A
703 181.15 75.33 Grey B
704 172.05 80.74 Brown B
705 178.06 87.39 Brown A
706 158.88 73.42 Blue B
707 169.57 85.41 Grey A
708 168.34 91.51 Brown B
709 166.92 104.46 Grey A
710 162.76 76.71 Grey B
711 164.92 88.80 Green A
712 172.33 66.96 Green B
713 170.21 83.83 Brown A
714 175.88 66.19 Brown B
715 175.74 78.63 Grey B
716 175.06 84.60 Brown A
717 170.22 82.79 Grey A
718 163.41 72.84 Brown B
719 167.81 69.18 Brown B
720 170.05 70.25 Brown A
721 161.73 57.69 Blue B
722 187.40 80.36 Blue B
723 178.57 84.51 Green A
724 168.97 84.38 Grey A
725 176.59 77.63 Brown A
726 168.18 74.67 Brown B
727 179.48 64.46 Brown A
728 161.75 95.80 Grey A
729 168.11 76.98 Brown B
730 174.14 80.32 Green B
731 164.47 90.74 Brown B
732 160.48 68.74 Brown A
733 165.24 65.82 Green B
734 179.93 76.49 Grey B
735 169.37 65.14 Blue B
736 177.01 82.25 Blue B
737 171.66 89.68 Grey A
738 161.98 83.14 Blue A
739 182.92 68.73 Grey B
740 175.51 77.38 Green B
741 165.45 94.28 Green B
742 175.55 89.13 Grey A
743 171.25 81.51 Grey A
744 173.31 81.15 Grey A
745 169.20 83.91 Blue B
746 176.58 64.95 Brown B
747 177.51 58.00 Brown B
748 157.56 72.30 Green A
749 180.94 88.69 Green A
750 160.33 89.71 Green A
751 172.03 75.78 Blue B
752 177.04 82.96 Blue B
753 169.15 71.61 Green B
754 165.06 69.66 Grey A
755 170.48 93.27 Grey A
756 165.01 77.70 Grey A
757 171.92 65.34 Brown A
758 170.18 68.41 Green B
759 164.87 81.80 Grey A
760 168.39 87.68 Grey B
761 162.04 77.53 Brown A
762 177.38 90.14 Brown A
763 176.05 82.96 Green B
764 185.33 97.28 Green B
765 172.98 87.51 Brown B
766 174.89 68.85 Grey B
767 174.46 76.35 Grey B
768 171.37 68.31 Grey A
769 171.27 94.03 Green A
770 168.07 90.74 Brown A
771 174.33 57.42 Brown A
772 174.21 80.50 Green A
773 167.70 66.39 Green B
774 164.26 80.39 Grey A
775 186.83 79.01 Brown B
776 174.32 83.73 Grey A
777 173.50 92.93 Brown B
778 169.33 69.16 Green B
779 176.49 67.70 Grey A
780 170.68 85.13 Green B
781 169.74 67.86 Grey A
782 162.16 91.99 Green A
783 175.25 87.20 Green A
784 182.75 79.18 Grey B
785 170.20 59.65 Green A
786 164.19 88.33 Green A
787 163.85 91.10 Green A
788 164.92 82.03 Brown B
789 178.15 85.93 Grey B
790 163.24 88.94 Brown A
791 165.46 86.33 Blue B
792 172.60 83.24 Brown A
793 167.47 81.87 Brown A
794 171.98 91.66 Green B
795 179.25 69.31 Grey B
796 172.06 74.56 Brown B
797 166.93 78.48 Grey A
798 172.85 63.76 Grey B
799 165.20 78.90 Grey B
800 179.49 88.48 Blue B
801 174.78 65.54 Blue B
802 168.69 70.52 Brown A
803 180.63 82.52 Blue B
804 172.99 100.94 Green B
805 165.76 67.77 Green A
806 166.49 82.86 Blue B
807 169.43 57.92 Brown A
808 171.73 81.76 Green A
809 163.62 88.36 Blue B
810 159.71 86.31 Green B
811 182.76 82.51 Brown A
812 161.47 72.81 Brown A
813 173.19 75.70 Green A
814 163.44 86.56 Brown B
815 176.67 60.29 Blue B
816 163.43 97.09 Grey B
817 173.28 76.30 Green B
818 172.58 83.69 Grey B
819 164.32 77.01 Brown A
820 168.22 67.88 Blue A
821 150.92 77.64 Brown B
822 172.76 80.55 Blue A
823 164.35 73.69 Green B
824 165.69 75.06 Grey B
825 176.16 84.56 Grey B
826 157.74 88.40 Green A
827 170.35 76.74 Green A
828 183.95 80.39 Blue A
829 162.00 78.95 Blue A
830 181.28 66.60 Green B
831 174.39 56.65 Grey A
832 159.20 86.40 Grey B
833 174.50 65.25 Brown A
834 163.03 80.33 Blue A
835 167.41 80.36 Brown B
836 165.03 89.11 Grey B
837 179.04 87.35 Blue B
838 161.36 78.58 Green B
839 166.11 68.33 Brown A
840 168.41 71.24 Green B
841 171.07 85.61 Grey B
842 175.04 61.38 Grey B
843 174.98 68.79 Brown A
844 164.68 86.80 Green B
845 166.59 82.69 Brown A
846 159.65 74.14 Brown A
847 179.09 91.54 Green B
848 164.22 78.42 Green B
849 164.55 85.67 Grey A
850 182.11 92.52 Green A
851 174.90 93.75 Green A
852 172.54 88.82 Blue A
853 170.84 77.66 Blue A
854 175.22 68.17 Blue B
855 175.12 71.78 Blue A
856 162.62 89.11 Blue B
857 170.29 79.53 Brown B
858 174.84 61.45 Grey B
859 173.65 82.97 Green B
860 164.60 86.46 Green B
861 178.36 54.60 Green A
862 164.19 83.58 Blue B
863 157.51 82.66 Brown B
864 174.13 76.87 Brown A
865 165.17 64.90 Green B
866 177.45 63.20 Brown B
867 167.33 74.84 Grey A
868 175.80 81.74 Green A
869 172.49 81.38 Green A
870 162.09 78.26 Green A
871 173.98 78.24 Grey A
872 171.09 74.43 Blue A
873 167.84 69.64 Green A
874 168.60 70.73 Blue B
875 163.46 81.89 Blue A
876 177.19 79.26 Blue B
877 161.45 58.22 Grey B
878 174.31 69.15 Grey A
879 172.42 72.58 Brown B
880 167.85 80.45 Grey B
881 168.74 99.20 Green A
882 165.86 80.97 Brown A
883 169.62 70.98 Green B
884 167.87 84.41 Green A
885 165.95 98.69 Blue A
886 155.84 79.45 Grey B
887 171.42 78.69 Blue B
888 171.14 106.46 Blue B
889 168.84 88.28 Green A
890 175.91 66.87 Green B
891 175.18 81.04 Grey B
892 171.30 80.72 Blue A
893 165.17 71.09 Grey B
894 178.78 88.12 Green A
895 174.62 71.12 Grey A
896 170.26 68.25 Green A
897 179.31 58.19 Green A
898 180.51 96.41 Blue A
899 173.53 92.05 Brown B
900 165.74 76.31 Grey A
901 176.17 87.32 Brown A
902 167.82 88.80 Brown B
903 164.41 85.48 Green B
904 161.65 87.52 Grey B
905 163.57 90.17 Grey B
906 163.10 90.68 Green A
907 170.69 87.38 Grey A
908 167.90 84.00 Green B
909 174.47 80.93 Green B
910 172.46 93.12 Green A
911 169.07 65.93 Grey A
912 171.98 77.01 Grey B
913 166.94 75.92 Green A
914 168.10 73.89 Green A
915 168.69 74.37 Blue A
916 174.00 77.32 Brown B
917 156.31 75.34 Brown A
918 155.59 81.60 Green B
919 162.65 80.18 Grey B
920 163.22 84.07 Green B
921 166.35 80.21 Brown B
922 173.69 72.18 Brown A
923 177.07 54.74 Green B
924 186.69 61.83 Blue A
925 167.84 68.31 Blue B
926 162.95 83.75 Grey B
927 170.66 65.66 Grey A
928 169.88 71.46 Green A
929 173.43 69.61 Brown B
930 165.00 77.79 Blue B
931 174.13 90.35 Brown B
932 171.46 73.28 Brown A
933 164.49 82.80 Green A
934 152.30 75.36 Green A
935 174.43 87.18 Blue A
936 165.58 102.13 Blue A
937 160.29 77.79 Green B
938 170.25 86.01 Grey A
939 177.55 91.71 Grey A
940 164.84 94.45 Blue A
941 164.07 79.20 Green B
942 166.57 84.99 Blue B
943 161.47 97.52 Grey B
944 173.55 85.37 Blue A
945 163.59 81.39 Grey A
946 162.13 76.12 Blue A
947 163.10 88.56 Blue B
948 170.11 57.10 Green A
949 166.96 79.89 Grey A
950 172.18 77.77 Grey B
951 165.04 74.91 Blue A
952 169.23 82.95 Blue A
953 170.65 69.72 Blue A
954 173.66 76.40 Brown B
955 162.64 65.73 Brown A
956 163.84 80.17 Brown B
957 163.12 102.35 Blue A
958 163.57 82.56 Brown B
959 169.02 75.04 Green B
960 176.90 62.60 Brown A
961 164.87 73.71 Green B
962 183.08 79.86 Brown A
963 175.47 80.01 Blue A
964 168.96 77.69 Grey A
965 167.64 87.86 Green A
966 175.09 75.73 Blue A
967 166.50 82.40 Brown B
968 181.62 79.34 Green A
969 183.81 67.89 Grey B
970 182.15 80.46 Green B
971 166.94 87.38 Blue A
972 172.27 110.86 Blue A
973 168.78 62.85 Green A
974 159.33 84.94 Brown B
975 169.17 90.67 Brown B
976 159.78 106.06 Blue A
977 169.47 88.83 Green A
978 168.82 92.05 Grey B
979 169.06 74.83 Blue B
980 174.91 70.33 Green B
981 176.09 81.09 Green B
982 162.05 86.69 Blue A
983 168.60 76.24 Green B
984 171.85 80.32 Green B
985 168.91 89.18 Green B
986 170.05 89.86 Brown A
987 163.26 80.00 Brown A
988 174.87 90.83 Brown B
989 163.92 83.57 Blue B
990 166.18 85.91 Grey B
991 180.81 68.73 Grey A
992 171.91 90.01 Green B
993 176.89 76.97 Blue B
994 174.08 59.10 Blue B
995 156.06 102.07 Green B
996 163.94 85.15 Grey A
997 161.96 68.63 Blue B
998 169.91 81.64 Brown A
999 165.87 71.79 Grey A
1000 156.67 86.92 Grey B

How similar are these groups?

Let’s first check their heights:

How similar are these groups?

And their weights:

How similar are these groups?

And their eye colors:

Making sure this wasn’t a fluke

Let’s re-run this:

ID Height Weight Eye colour Group
1 164.26 52.92 Green A
2 166.89 84.08 Grey B
3 173.48 76.97 Brown B
4 170.48 84.42 Blue B
5 175.38 86.80 Green A
6 167.74 73.26 Blue B
7 176.89 78.91 Blue B
8 170.59 86.85 Brown A
9 176.90 84.77 Blue B
10 171.01 69.88 Grey A
11 168.57 71.46 Blue B
12 170.08 83.52 Green A
13 169.57 69.79 Grey A
14 168.58 74.14 Grey B
15 167.81 75.07 Grey A
16 171.51 60.62 Brown B
17 170.24 60.93 Brown B
18 171.78 74.47 Grey A
19 180.18 93.82 Blue A
20 173.31 83.43 Green A
21 161.92 99.96 Grey A
22 173.14 74.92 Green A
23 175.69 79.47 Brown A
24 181.84 94.84 Green B
25 165.85 91.22 Grey A
26 168.48 76.40 Green A
27 178.39 68.96 Grey B
28 174.01 83.72 Brown A
29 181.95 78.79 Brown B
30 171.50 73.69 Blue B
31 158.98 88.57 Green A
32 175.80 82.91 Grey B
33 177.61 62.68 Green B
34 170.61 66.02 Blue B
35 165.31 70.63 Blue A
36 171.15 65.33 Brown B
37 175.04 88.20 Grey A
38 172.63 66.92 Grey A
39 174.24 77.46 Grey A
40 171.23 72.70 Green A
41 181.85 76.38 Brown A
42 169.84 72.25 Brown A
43 178.83 86.12 Grey A
44 180.32 69.69 Brown A
45 168.65 72.67 Green A
46 162.35 57.10 Blue B
47 152.79 78.98 Grey B
48 172.59 83.20 Green A
49 173.95 75.92 Blue B
50 175.94 90.79 Green B
51 167.77 68.77 Green B
52 164.13 70.63 Blue A
53 175.30 75.30 Grey A
54 168.81 88.19 Green B
55 167.47 83.78 Brown A
56 168.07 74.57 Blue B
57 157.69 60.87 Blue A
58 164.92 74.49 Brown A
59 171.48 75.50 Brown B
60 157.84 79.47 Green A
61 174.07 86.33 Brown A
62 161.46 70.05 Grey A
63 170.23 80.54 Blue B
64 170.85 90.98 Grey A
65 178.94 74.48 Grey A
66 173.93 64.49 Blue A
67 173.22 67.79 Brown A
68 175.84 71.85 Blue A
69 170.90 93.90 Green A
70 160.68 69.41 Blue A
71 171.09 79.61 Blue B
72 180.43 79.34 Green A
73 163.23 107.84 Brown B
74 163.43 72.68 Grey B
75 166.36 92.99 Green B
76 168.49 91.05 Brown B
77 174.75 84.66 Grey A
78 162.17 91.25 Brown A
79 166.22 93.94 Blue A
80 164.78 89.26 Green B
81 169.83 67.22 Blue A
82 166.89 67.41 Grey B
83 167.84 71.53 Grey B
84 170.30 64.05 Brown B
85 179.13 72.42 Green B
86 161.91 71.91 Brown A
87 180.92 85.47 Grey B
88 168.68 63.92 Green A
89 176.12 77.45 Brown B
90 173.75 89.11 Grey B
91 170.31 85.81 Grey A
92 168.86 95.05 Green B
93 163.84 68.41 Blue B
94 177.13 61.98 Grey B
95 163.91 80.01 Brown A
96 163.38 79.99 Green B
97 176.37 71.59 Green B
98 169.32 80.25 Blue A
99 171.38 68.90 Green B
100 169.38 74.83 Brown A
101 159.26 68.96 Blue B
102 175.53 97.56 Brown B
103 167.83 92.94 Green A
104 162.05 81.22 Brown B
105 175.16 106.42 Grey A
106 180.76 77.06 Green B
107 173.87 92.64 Green B
108 174.65 87.64 Blue B
109 162.87 71.05 Grey A
110 162.27 81.45 Green A
111 158.18 92.18 Blue A
112 169.17 88.93 Blue B
113 164.27 71.72 Grey A
114 178.32 98.51 Green B
115 172.85 89.73 Grey B
116 171.98 68.07 Blue B
117 170.44 77.68 Brown B
118 180.69 62.29 Blue A
119 173.25 76.62 Blue B
120 177.39 81.99 Brown A
121 175.96 83.15 Grey A
122 168.64 83.43 Blue A
123 172.87 69.10 Blue B
124 174.24 74.36 Green A
125 163.52 89.09 Blue B
126 173.86 91.25 Grey A
127 166.18 75.99 Green B
128 167.58 87.40 Grey A
129 177.98 66.90 Green A
130 168.78 95.97 Brown B
131 166.73 80.93 Grey B
132 169.20 81.77 Blue A
133 181.24 53.61 Blue A
134 167.48 78.43 Grey A
135 172.15 77.08 Green A
136 164.70 74.33 Brown B
137 172.92 78.59 Blue B
138 165.45 86.66 Grey A
139 174.56 79.11 Grey B
140 177.11 80.03 Blue B
141 173.38 82.32 Blue A
142 168.58 86.63 Green A
143 172.66 74.01 Brown A
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323 155.74 81.77 Grey A
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364 163.87 105.01 Blue A
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367 175.51 56.87 Brown A
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370 167.84 85.77 Green A
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373 177.31 66.59 Green A
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378 161.43 71.33 Blue B
379 166.05 62.82 Green B
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391 163.69 74.08 Green A
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399 167.99 75.53 Brown B
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403 165.50 72.46 Grey A
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411 164.93 62.11 Green B
412 183.56 88.33 Brown B
413 174.70 88.68 Blue A
414 162.23 64.36 Green A
415 182.68 86.08 Brown A
416 165.07 83.41 Brown A
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419 164.02 102.66 Grey A
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423 175.17 63.84 Brown A
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431 162.43 90.14 Grey A
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435 162.29 85.64 Blue A
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438 165.91 80.92 Green A
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440 160.78 83.18 Grey B
441 178.63 76.45 Green B
442 170.41 81.38 Blue A
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482 158.29 101.64 Grey A
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491 173.36 88.68 Grey B
492 167.22 93.74 Brown A
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495 162.47 80.31 Grey B
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515 168.88 57.29 Grey A
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519 181.13 89.54 Grey A
520 184.31 108.73 Blue B
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522 165.63 91.33 Grey A
523 176.27 69.51 Green A
524 167.91 77.48 Blue B
525 171.15 70.10 Brown A
526 168.91 76.16 Blue A
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529 161.70 76.32 Green A
530 169.87 80.65 Green B
531 169.24 68.92 Grey B
532 167.44 81.36 Blue A
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535 173.13 96.14 Blue B
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539 174.58 76.04 Brown B
540 175.88 79.06 Blue B
541 167.46 78.88 Green B
542 173.78 60.94 Grey A
543 179.62 73.93 Blue A
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546 165.26 83.74 Blue B
547 164.43 81.78 Blue A
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550 176.46 88.36 Grey B
551 165.81 78.63 Grey A
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565 163.11 78.19 Green B
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570 162.83 71.56 Blue B
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572 167.53 76.30 Blue A
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575 179.40 92.09 Blue A
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580 176.27 90.02 Green A
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583 171.54 88.16 Blue A
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585 176.18 84.41 Blue A
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588 163.15 84.83 Green B
589 162.23 59.97 Green A
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591 171.76 73.92 Brown B
592 172.66 101.87 Grey A
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594 169.99 99.69 Blue A
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629 176.29 82.04 Grey A
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631 174.35 80.32 Green A
632 173.15 64.97 Grey A
633 175.28 73.25 Green A
634 167.41 67.19 Brown A
635 164.19 89.81 Brown B
636 183.06 93.59 Blue B
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641 164.96 75.14 Blue B
642 161.02 78.67 Blue B
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646 164.82 81.66 Blue B
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651 169.40 70.44 Grey B
652 180.18 76.36 Brown B
653 166.35 84.95 Green B
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655 169.50 84.78 Blue B
656 166.27 97.93 Grey B
657 176.14 75.50 Green B
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662 164.27 63.70 Blue A
663 171.16 75.64 Blue B
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665 164.42 96.20 Green A
666 175.12 84.65 Blue A
667 165.84 45.42 Blue A
668 182.88 89.95 Grey A
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671 179.85 86.00 Blue B
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698 174.93 60.05 Grey B
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702 169.96 90.92 Brown B
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706 158.88 73.42 Blue A
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709 166.92 104.46 Grey B
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713 170.21 83.83 Brown B
714 175.88 66.19 Brown B
715 175.74 78.63 Grey B
716 175.06 84.60 Brown B
717 170.22 82.79 Grey B
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719 167.81 69.18 Brown B
720 170.05 70.25 Brown A
721 161.73 57.69 Blue B
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723 178.57 84.51 Green B
724 168.97 84.38 Grey B
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731 164.47 90.74 Brown A
732 160.48 68.74 Brown B
733 165.24 65.82 Green B
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735 169.37 65.14 Blue A
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737 171.66 89.68 Grey B
738 161.98 83.14 Blue A
739 182.92 68.73 Grey A
740 175.51 77.38 Green B
741 165.45 94.28 Green A
742 175.55 89.13 Grey A
743 171.25 81.51 Grey B
744 173.31 81.15 Grey B
745 169.20 83.91 Blue A
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747 177.51 58.00 Brown B
748 157.56 72.30 Green A
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750 160.33 89.71 Green B
751 172.03 75.78 Blue B
752 177.04 82.96 Blue B
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764 185.33 97.28 Green A
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766 174.89 68.85 Grey A
767 174.46 76.35 Grey A
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769 171.27 94.03 Green A
770 168.07 90.74 Brown B
771 174.33 57.42 Brown B
772 174.21 80.50 Green B
773 167.70 66.39 Green B
774 164.26 80.39 Grey A
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776 174.32 83.73 Grey B
777 173.50 92.93 Brown A
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781 169.74 67.86 Grey A
782 162.16 91.99 Green A
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785 170.20 59.65 Green A
786 164.19 88.33 Green B
787 163.85 91.10 Green B
788 164.92 82.03 Brown B
789 178.15 85.93 Grey B
790 163.24 88.94 Brown B
791 165.46 86.33 Blue B
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793 167.47 81.87 Brown A
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795 179.25 69.31 Grey B
796 172.06 74.56 Brown A
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799 165.20 78.90 Grey A
800 179.49 88.48 Blue A
801 174.78 65.54 Blue A
802 168.69 70.52 Brown B
803 180.63 82.52 Blue B
804 172.99 100.94 Green A
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810 159.71 86.31 Green A
811 182.76 82.51 Brown B
812 161.47 72.81 Brown B
813 173.19 75.70 Green A
814 163.44 86.56 Brown A
815 176.67 60.29 Blue A
816 163.43 97.09 Grey A
817 173.28 76.30 Green A
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819 164.32 77.01 Brown A
820 168.22 67.88 Blue B
821 150.92 77.64 Brown A
822 172.76 80.55 Blue A
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826 157.74 88.40 Green B
827 170.35 76.74 Green B
828 183.95 80.39 Blue B
829 162.00 78.95 Blue B
830 181.28 66.60 Green A
831 174.39 56.65 Grey A
832 159.20 86.40 Grey B
833 174.50 65.25 Brown B
834 163.03 80.33 Blue A
835 167.41 80.36 Brown B
836 165.03 89.11 Grey B
837 179.04 87.35 Blue A
838 161.36 78.58 Green A
839 166.11 68.33 Brown B
840 168.41 71.24 Green A
841 171.07 85.61 Grey B
842 175.04 61.38 Grey B
843 174.98 68.79 Brown A
844 164.68 86.80 Green B
845 166.59 82.69 Brown B
846 159.65 74.14 Brown B
847 179.09 91.54 Green B
848 164.22 78.42 Green A
849 164.55 85.67 Grey A
850 182.11 92.52 Green A
851 174.90 93.75 Green B
852 172.54 88.82 Blue B
853 170.84 77.66 Blue A
854 175.22 68.17 Blue B
855 175.12 71.78 Blue A
856 162.62 89.11 Blue B
857 170.29 79.53 Brown B
858 174.84 61.45 Grey A
859 173.65 82.97 Green B
860 164.60 86.46 Green A
861 178.36 54.60 Green A
862 164.19 83.58 Blue B
863 157.51 82.66 Brown B
864 174.13 76.87 Brown B
865 165.17 64.90 Green A
866 177.45 63.20 Brown A
867 167.33 74.84 Grey A
868 175.80 81.74 Green B
869 172.49 81.38 Green B
870 162.09 78.26 Green A
871 173.98 78.24 Grey A
872 171.09 74.43 Blue A
873 167.84 69.64 Green B
874 168.60 70.73 Blue A
875 163.46 81.89 Blue A
876 177.19 79.26 Blue B
877 161.45 58.22 Grey A
878 174.31 69.15 Grey A
879 172.42 72.58 Brown A
880 167.85 80.45 Grey B
881 168.74 99.20 Green A
882 165.86 80.97 Brown A
883 169.62 70.98 Green A
884 167.87 84.41 Green B
885 165.95 98.69 Blue B
886 155.84 79.45 Grey A
887 171.42 78.69 Blue A
888 171.14 106.46 Blue B
889 168.84 88.28 Green A
890 175.91 66.87 Green B
891 175.18 81.04 Grey B
892 171.30 80.72 Blue B
893 165.17 71.09 Grey B
894 178.78 88.12 Green A
895 174.62 71.12 Grey B
896 170.26 68.25 Green A
897 179.31 58.19 Green A
898 180.51 96.41 Blue B
899 173.53 92.05 Brown A
900 165.74 76.31 Grey A
901 176.17 87.32 Brown A
902 167.82 88.80 Brown A
903 164.41 85.48 Green B
904 161.65 87.52 Grey B
905 163.57 90.17 Grey A
906 163.10 90.68 Green B
907 170.69 87.38 Grey B
908 167.90 84.00 Green B
909 174.47 80.93 Green B
910 172.46 93.12 Green A
911 169.07 65.93 Grey A
912 171.98 77.01 Grey B
913 166.94 75.92 Green B
914 168.10 73.89 Green B
915 168.69 74.37 Blue B
916 174.00 77.32 Brown B
917 156.31 75.34 Brown A
918 155.59 81.60 Green A
919 162.65 80.18 Grey B
920 163.22 84.07 Green B
921 166.35 80.21 Brown A
922 173.69 72.18 Brown A
923 177.07 54.74 Green A
924 186.69 61.83 Blue B
925 167.84 68.31 Blue B
926 162.95 83.75 Grey A
927 170.66 65.66 Grey B
928 169.88 71.46 Green A
929 173.43 69.61 Brown B
930 165.00 77.79 Blue A
931 174.13 90.35 Brown B
932 171.46 73.28 Brown A
933 164.49 82.80 Green B
934 152.30 75.36 Green A
935 174.43 87.18 Blue A
936 165.58 102.13 Blue B
937 160.29 77.79 Green A
938 170.25 86.01 Grey A
939 177.55 91.71 Grey B
940 164.84 94.45 Blue B
941 164.07 79.20 Green B
942 166.57 84.99 Blue A
943 161.47 97.52 Grey A
944 173.55 85.37 Blue A
945 163.59 81.39 Grey B
946 162.13 76.12 Blue B
947 163.10 88.56 Blue A
948 170.11 57.10 Green B
949 166.96 79.89 Grey A
950 172.18 77.77 Grey B
951 165.04 74.91 Blue B
952 169.23 82.95 Blue A
953 170.65 69.72 Blue A
954 173.66 76.40 Brown A
955 162.64 65.73 Brown B
956 163.84 80.17 Brown B
957 163.12 102.35 Blue B
958 163.57 82.56 Brown A
959 169.02 75.04 Green A
960 176.90 62.60 Brown A
961 164.87 73.71 Green A
962 183.08 79.86 Brown A
963 175.47 80.01 Blue B
964 168.96 77.69 Grey B
965 167.64 87.86 Green B
966 175.09 75.73 Blue B
967 166.50 82.40 Brown A
968 181.62 79.34 Green A
969 183.81 67.89 Grey B
970 182.15 80.46 Green B
971 166.94 87.38 Blue A
972 172.27 110.86 Blue A
973 168.78 62.85 Green B
974 159.33 84.94 Brown B
975 169.17 90.67 Brown A
976 159.78 106.06 Blue A
977 169.47 88.83 Green A
978 168.82 92.05 Grey B
979 169.06 74.83 Blue A
980 174.91 70.33 Green A
981 176.09 81.09 Green A
982 162.05 86.69 Blue B
983 168.60 76.24 Green A
984 171.85 80.32 Green A
985 168.91 89.18 Green B
986 170.05 89.86 Brown B
987 163.26 80.00 Brown A
988 174.87 90.83 Brown A
989 163.92 83.57 Blue B
990 166.18 85.91 Grey A
991 180.81 68.73 Grey A
992 171.91 90.01 Green B
993 176.89 76.97 Blue A
994 174.08 59.10 Blue B
995 156.06 102.07 Green A
996 163.94 85.15 Grey B
997 161.96 68.63 Blue A
998 169.91 81.64 Brown A
999 165.87 71.79 Grey B
1000 156.67 86.92 Grey A

Check how similar they are

Increasingly similar

In fact, if we did this many, many, many times, these groups would be, on average, increasingly identical!

Why?

  • Central limit theorem

  • Law of large numbers

Do international monitors deter election-day fraud?

Yes!

  • The international community monitored the 2003 Armenian Presidential elections
  • Monitors were assigned randomly to the polling stations
  • Hyde found a big average difference between the vote share received by the cheating party at monitored stations compared to non-monitored stations.